Device for determining azimuth by observations on polaris



Jan.- 9, 1934. s. GUTTORMSSON 1,942,543

DEVICE FOR DETERMINING AZIMUIH BY OBSERVATIONS ON POLARIS Filed March 23, 1935 Jail-MM 5mm Patented Jan. 9, 1934 UNETED STATES PATENT OFFICE DEVICE FCDR DETER MHNIING AZEMUTH BY OBSERVATIQNS ON POLARIS Application March 23,

1933, Serial No. 662,280,

and in Canada March 2, 1933 1 Claim.

My invention relates to the inscription of a series of concentric circles, four being the most convenient number for my purpose, on the diaphragm in the reticule of the telescope having a suificiently large field of view of such surveyors instruments as are equipped with such diaphragms in their reticules, and the inscribing of graduations and figures denoting time intervals thereon, which said diaphragms may be of glass or other suitable substance, and which, as is well known, are inserted in the telescope of surveying instruments; or in the case of surveying instru ments whose telescopes have the proper field. of view, but are not equipped with diaphragms in their reticules, the inscription of said concentric circles on a diaphragm together with the graduations and figures denoting time intervals, especially constructed for use with them; the said concentric circles with their attendant gradnations and figures denoting time intervals being used in conjunction with the formulae herein set forth by which observations on Polaris for azimuth may be made with a minimum of calculation without any timepiece except an ordinary watch set to keep civil time. I attain these objects by the artifices and formula illustrated in the accompanying drawing, in which:

Figure 1 shews a typical reticule of a surveyors transit equipped with a glass diaphragm on which have been inscribed, in addition to the customary vertical and horizontal lines, the series of concentric circles, which circles constitute the major part of my invention.

Figure 2 shews, on an enlarged scale the said concentric circles, and graduations and figures denoting time intervals.

Figure 3 shews in their proper places, and designates, the geometrical elements which enter 40 into the derivation of the formulae.

Figures 4 and 5 shew the positions of Polaris in the various quadrants. I

Similar letters and figures refer to similar parts throughout the drawing.

Referring to the drawing:-

1 represents the metal ring of the reticule with the four adjusting screws, 2 represents the diaphragm fastened to the ring of the reticule. 3 and 4 represent, respectively, the vertical and horizontal lines inscribed on the diaphragm. But as these features do not constitute my invention, no further description of them is necessary. 5 represents the series of circles having for a common centre the point of intersection of the vertical and horizontal lines 3 and 4. (In Figure 1 these concentric circles are not shewn separately, but are represented by one heavy black circle.) In Figure 2 which is drawn to an enlarged scale, 5 represents the four concentric circles with radii f tan(ao'30") and f tan(a130), where f is the focal length of the object glass of the transit instrument, and or, to the nearest onehalf minute, the average co-declination of Polaris for a certain ten-year period. For the decade ending December 31st, A. D. 19 39, or equals one degree, two minutes, and thirty seconds (1 02 30"). For subsequent decades new diaphragms will have to be prepared in accordance with my invention.

The marks 6 represent divisions of astronomical time, the space between the smallest divisions representing ten minutes.

The figures 7 6 etc. on the outside ofv the outermost circle represent certain intervals of civil time calculated from the formula:

where h represents the hour-angle of Polaris reckoned east or west from the upper or lower culmination, according to the quadrant in which Polaris happens to be situated. (dh) seconds of arc are then converted into seconds of civil time by multiplying by Referring to Figure 3, (db) represents the seconds of are that Polaris must travel in order that wherem", 62" are the seconds of are by which the co-declination of Polaris exceeds or falls short of the arcual radii of the adjacent circles of the series between which said co-declination lies; and where m1, 1112" are the angles which true north makes with the two directions of the telescope conditioned by the two circles in question. This formula is approximate only, but gives values within two seconds of are when h is not less than fifteen degrees, and when the latitude of the place of observation is not greater than seventy-five degrees. This formula constitutes a prominent feature of my invention. Its derivation from Figure 3 is given below:,

may be equal to Derivation of formulae Referring to Figure 3, p represents the polar distance of Polaris; -i-el", and -fia", the

arcual radii of the critical circles; h the hour angle of Polaris; m1", m2" angular deviations due to 51" and 62 measured on the small circle in the heavens with the zenith as centre. These fifteen degrees and L equals seventy-five degrees, give rise to an error greater than about two seconds the azimuth. So that all the errors involved in the various approximations, if of the 5 angular deviations measured on the horizon same sign, may cause a maximum error of two 80 would be m1" secL and 'mz" secL where L seconds in azimuth. is the latitude of the place of observation. 0 As Polaris will he closest to the celestial pole represents the celestial pole and C the upper 0111- in the year 2102, when its cc-declination will be mination. We find a formula for (dh) in order about twenty-seven minutes and thirty-seven that the ratio seconds (27' 37"), there is no danger, for some 85 6 time to come, of this method becoming useless. W After the year 2102, Polaris will gradually recede from the pole until its co-declination will have may become apprommately equal to the who become so great that no field of view or" any sur- Q2 veyors instrument, will, with one pointing, com- 90 2 prise the whole of its journey around the pole. At the outset we make certain assumptions: (a) The fllowing its the practical exposition of my P is the average co-declination of Polaris for the ten-year period; (b) m1 and 1m are considered The Surveyor W111 have to know the arcs f great circlea While these assumptions tion of Polaris for the day of the observation, 95 lead to small errors, it may be shewn that these, heme he Win hays to be Supplied with in the most f bl cases, when the hour cal Almanac, or ephemeris, or something equivaangle of Polaris is fifteen degrees and the lati- He must also be provided with Watch u seventyfive degrees do not produce any regulated to keep accurate civil time. This, asappreciable error in the azimuth. surning on his part a knowledge of the approxi- 106 We are now ready to deduce our formula mate longitude of his place of observation, will I enable him to predict from information supplied COS P m1 5m P Sm m1 COS in the almanac or ephemeris what the approxicos (p'-5 )=C0S p cos m +sin p sin m cos g mate hour-angle or Polaris will be at any given (cos p cos 5 sin p sin 5,) sin m local civil time. It is also necessary for the 105 cos p cos m1 Sin mz sin p Sin m1 Sin m2 COS g1 surveyor to know the latitude of the place of d observation as accurately as the degree of pre- (cos p cos 5 +sin p sin 5 sin m cision desired'in the determination of the azicos p cos m sin m +sin p sin in; sin m cosg ninth warrants. This, in surveyed territory, .'.cos p [cos 5 sin m +cos 5 sin m ]+sin p[sin m sin 6 i m2 i 5 3 cos pirru-trrm-Wji-sin p sin n1 sin m 2 sin sin 40 But ce W W n he Condition under which every surveyor will know. In unsurveyed terriw 51 1 tory the usual observat ons of Polaris at upper equals or lower culmination, or both, will supply the surveyor with the desired information. or, since all the angles are small, under which If Polaris is Very near the upper or lower Sin 51 Sin ml culmination-say within 15 of are, or one hour Sin 52 I 7 3 in 1me-the method fails. At all other times, Whenever the usual methods of observation on We can p out the m Polaris are applicable, the method herein outsin'p [Sin m1 Sin m2 sin 51] lined is also applicable. The surveyor then prof ceeds as follows: rom the last equation. Dolng this, expanding,

and using the relation To find the azimuth of a given Zine t equals m First, knowing the arcual radii of the series or 6 2 circles, he knows the two circles whose arcual h radii are, one, the next greater, and the other, 136;

3 3 2 3 cos p[m lm cos p [m +m 7 sin p sin m sin m 2 cos sin cc' We can put:- the next less, than the co-declination of Polaris.

61 52 61+52 Let these two circles be'calledthe outer and inequals =-'-=sin 21, nor critical circles. (11 the polar distance of m1 m2 m1+m2 Polaris happens to be exactly the'radius of one approximately. Hence after easy deductions of these circles, the process is so much simpli- 3146 5 -1-5 cos 1':

2 sin I:

h There are approximations used in this derivation, but these can never, even'for h equals 6 sin h to I lied.) Set the alidade to zero and clamp. Sight telescope on reference object on the ground. Clamp lower limb. Lay ofi on vertical circle latitude refraction of the pole, (if great accuracy is' desired We make a correction in refraction for the situation of Polaris above or below the pole, which can be obtained graphically, as we know beforehand fairly accurately where Polaris is situated.) Loosen the upper clamp. -Turn alidade until Polaris is in the proper quadrant between the critical circles. Then clamp alidade and with the upper slow motion screw move the alidade until the outer critical circle bisects the image of Polaris, if the said image of Polaris occupies either of the two positions indicated in Figure 4; or until the inner critical circle bisects the image of Polaris, if the said image of Polaris occupies either of the two positions indicated in Figure 5. Read the horizontal circle; if Polaris is seen opposite the mark or graduation, 5 Figure 2, then wait five minutes. At the expiration of this time interval, move the alidade by the upper slow motion screw until the image of Polaris is bisected by the inner critical circle, as indicated by the positions of the image of Polaris in Figure 4; or until the image of Polaris is bisected by the outer critical circle, as indicated by the positions of the image of Polaris in Figure 5. Read the horizontal circle. Then if a and b are the horizontal circle readings corresponding to the positions of Polaris on the outer and inner critical circles, as in Figure 4; or to the position of Polaris on the outer and inner critical circles, as in Figure 5; and if 61" and 62 are the differences between the codeclination of Polaris and the arcual radii of the corresponding critical circles, then the azimuth of the reference line equals:-

5 the signs To lay 017 on the ground a line having given a certain azimuth Set alidade to zero. Lay off on the vertical circle the latitude plus refraction of Polaris, as before. Turn the instrument by its lower slow motion screw so that the image of Polaris is bisected by the outer critical circle, if the image of Polaris occupies either of the two positions indicated in Figure 4; or until the inner critical circle bisects the said image of Polaris if it occupies either of the two positions indicated in Figure 5. If the image of Polaris is seen opposite the mark or graduation, say 4 Figure 2, then wait four minutes; and at the expiration of this time interval move the alidade by the upper slow motion until Polaris appears on the inner critical circle, being bisected thereby, as indicated by the positions of the image of Polaris in Figure 4; or until the image of Polaris is bisected by the outer critical circle, as indicated by the positions of the image of Polaris in Figure 5. Read horizontal circle of the instrument. Proportion as before, and by the upper slow motion make the horizontal circle read the corrected angle; the line is marked ofi on the ground in the usual manner. Reverse and repeat the process, as above outlined, to eliminate instrumental errors. Mark off on the ground the line corresponding to the reverse operations. Take the mean of the two lines so determined for the final line.

It is of course obvious that the reversing process here referred to applies only to the customary operations familiar to all surveyors and not to the critical circles.

The rules referred to above, relating to the positions of Polaris in the various quadrants, and embodied in Figures 4 and 5, are essentially the same for both erecting and inverting eye-pieces in the telescopes of surveyors instruments; and a corresponding rule for diagonal eye-pieces can easily be evolved.

I am aware that prior to my invention diaphragms, made of glass or other suitable substance have been used in the reticules of surveyors instruments, and that the ordinary vertical and horizontal cross lines have been ruled thereon. I therefore do not claim such a device; nor do I claim any means whereby lines, whether circular or curved may be ruled on glass or other suitable substance, which also applies to the graduations, or figures, or any combination thereof broadly; but:

I claim:

On a diaphragm to be inserted in the reticule of a surveyors instrument, or transit theodolite, the inscription of a series of concentric circles having radii determined in accordance with the formulae as set forth in the annexed specification, said circles having the graduations denoting time intervals for'use in conjunction with the said concentric circles, substantially as set forth.

STEPHAN GUTTORMSSON. 

